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We study the percolation and jamming of rods ($k$-mers) on a square latticethat contains defects. The point defects are placed randomly and uniformly onthe substrate before deposition of the rods. The general case of unequalprobabilities for orientation of depositing of rods along different directionsof the lattice is analyzed. Two different models of deposition are used. In therelaxation random sequential adsorption model (RRSA), the deposition of rods isdistributed over different sites on the substrate. In the single clusterrelaxation model (RSC), the single cluster grows by the random accumulation ofrods on the boundary of the cluster. For both models, a suppression of growthof the infinite cluster at some critical concentration of defects $d_c$ isobserved. In the zero defect lattices, the jamming concentration $p_j$ (RRSA)and the density of single clusters $p_s$ (RSC) decrease with increasing lengthrods and with a decrease in the order parameter. For the RRSA model, the valueof $d_c$ decreases for short rods as the value of $s$ increases. For longerrods, the value of $d_c$ is almost independent of $s$. Moreover, for shortrods, the percolation threshold is almost insensitive to the defectconcentration for all values of $s$. For the RSC model, the growth of clusterswith ellipse-like shapes is observed for non-zero values of $s$. The density ofthe clusters $p_s$ at the critical concentration of defects $d_c$ depends in acomplex manner on the values of $s$ and $k$. For disordered systems, the valueof $p_s$ tends towards zero in the limits of the very long rods and very smallcritical concentrations $d_c \to 0$. In this case, the introduction of defectsresults in a suppression of rods stacking and in the formation of `empty' orloose clusters with very low density. On the other hand, denser clusters areformed for ordered systems.

Percolation and jamming of linear $k$-mers on square lattice with defects: effect of anisotropy